Method for the preparation of density gradients



4, 1958 w. c. TAYLOR ETAL 2,825,698

METHOD FOR THE PREPARATION OF DENSITY GRADIENTS Filed Dec. 27, 1955 x bt QQ @www mxbgfw I INVENTORS. 1 Wi//f'am C. Tay/or l BY* Zub/o Tung mwfm ' HTTORNEY METHQD nonfarm PRLEBARMIoNoE-DENSIW William C, TaylorandgLu Ho Tung,l Midland,Mich., assigners to 'llflhe Bowl' Ghemial'Gompany; Midland, Mich., a.corporation-oielaware 11i claims. (ci. 25a-49s) This invention relates toapimproved' rnetholtfory the preparation. ofliquid columns which haveW a gradient. density from their 'lower to upper portions. k Y

Liquid-1 columns having agradient density are useful analytical implementsr which 'may be employed advantageously fori the quickand'w convenient` determination olf;`

the densities o r specific gravities of various materials. Such columns, which arefrequently known as density gradients, indicate the density-ory specific gravity of'ma-l terials which are immersed in thecolumn due to their floating in suspension, with equilibrium buoyancy, at a position in the column at which the speciiic gravity or density ofthe-.liquid inY the column andJ that off the'im mersed material'- are. in corres-pondence.v The application-- of density. gradients forl suchl purposeshas been somewhatl limited', however, because of the di'liicul-tywhich.

has been encountered in satisfactorily preparing them;

lt has been conventional practice inthe1 preparatiom of tion. to provide. an improved methodl. for theread-y: and/- convenient preparatiton of=more accurate.- density gradientshavinga substantially uniform rateof-density rchange` with height in the liquid column. The. methodt of: the present invention permits a greater practical adaptation of density gradients in ,analytical procedures. and-r in'i other applications by obviating manygoffthedicultiesand in conveniences attendant their., conventional preparation. Additional objects andi advantages are. alsor apparent throughout the speciticationand description.

According to the present. invention, a1 density` gradient comprised of a uniformly yvaryi1'1gmixture off two miscible` and compatible liquids having. different. densities can be preparedfreadily andin anexpeditious manneriby con tinuously changing therelativelproportions ofi'the, liquidsturewhile. transferring, without` turbulence',- ay stream o' the constantly. changing densityy mixture of the liquids,

to.a-columnar container; This-maybe=conveniently accomplished by continuous-ly;incorporating, atI ai uniform-` rate,'a rstliquid havingagiven density-vin; a mixture maintainedl at a substantially constant volume with a second liquidtwhich-.is-miscible andcompatible with, and` has a density diiierentvthanfthe-iirst liquid soy as to-constantly change the density ofl the mixa'nje;VA and continuouslyftransferring, without` turbulence, portionsv o fj the constantly` changing-- density mixtureltq a@ columnarY con- In addition, it is.- ant arduous.y and uncertainv nite States Patent O fl ce 2,825,698 Patentedr Mar. 45,.y 1.95.8

E rainer atI about thel same uniform rate, asl that. at which thel first liquid isl added to themixture. Advantageously the constantlyv changing density mixture can be continuou s ly, agitatedin an eicient manner which does. not inducev cavitation or bubblingxin` the mixture to insure a uniform incorporation of the first liquidv in the mixture with the second,

Optionally, thecolumnmay b e lled either from the topVV orbottom withjhe constant changing density mixture,4 It isnecessary for-the density gradient. to be inthe form` ofa liquidcolumn, having an upwardly decreasing gradient density.A Tothis. end, whentlie columnis being lledfrom the bottom, itis beneiicial to prepare the con,- stantly changing. density mixture by. adding a, heavier or greater density liquid tol an, initially major. orY total proportion. of a lighter.V or lower. density liquid in, the mixture so. thatr a` less. dense mixture of the liquids; will ultimately constitute the upper portion of the density gradient: Conversely, when, the column ist lled from the top'. it is. necessary. to. add a lighterliquid toy initially major, or total proportions, ofk a.- heavier liquid in the mixture. to insure the requisite downwardly increasing density 0f the densita gradient column.

Density. gradients prepared accordingtov the methodV of: the present invention, have-a substantially linear anduniform ratetof ehangein their'liquid, density throughout the height of @uniformly crossfsetioned; column. They may bia-employed; as soon asf desired;- after their preparation and.Y do4 not4 requireI longv and.l tedious preparation tech- IDQQES... Neillf iSzitznSSSary @wait-for the occurrence of sufficient interfacial' diiusion in order forY a usabledensity gradient to b eobtained: When handledV carefully/the density gradients are usefulfor prolonged periodsof timefbeforef theyare changed to uniformly. densel columnsvby diffusion of the mixed liquids. Frequentlyy theymay be employed satisfactorily for. periodsof months and; even; for ayear or longer. after. theirpreparation. In addition, they-permit the reliable-andex-tremely accurate measurement of the specicgravitiesk of various materials in` a quickandv eicient manner. In many instances, for example, density gradients can be prepared with whichL accurate measurements. to units as close as housandthsoffa gramper cubic centimeter can be o bctainedi,y Asgis obvious, they.A can alsobe employed to obtaina lesser,v accuracy-if suchuseis. satisfactory for the purposesfwhichmay. be. at hand:

Further.L illustration .ofn the, method of the present inventionis aorded-l in; the1 accompanying. drawing. wherein;

lfigur 1 represen ts,-an asscmblyof apparatus for preparingdensitygradients pursuant. to the method of.L thepresenttinvention- Figure;l 2j, seherrnviticallyt` represents an alternative` prod s;

A3; is a; graphdepicting typical characteristicsv of gradients preparedtaccording to the. inventan;

solution Nahavingpa densityl (g1),v containedV in a separat.

toryvfunnelftor-v like container) dischargeable at. accu:

etant rate-of-ll'owy (U1) tothe beaker 6,*wl1erein it 1sY mixed With-the quantity of liquid M in the beaker by an eicien-t stirring means such as a mixer 7 which agitates the liquids vigorously in order to. thoroughly mix them without inducing cavitation or bubbling. The` density ofrthemixture of-Ithe liquids Miand Nfixi thebeaker is,

constantly uniformly changed by the addition and mixing of the liquid N. The liquid mixture in the beaker is maintained substantially at a constant voliune (V) by means of its continuous withdrawal, as a constantly changing mixture G, having a constantly changing density (g) through a siphon tube 8 at a uniform rate of volume flow (U2) which is at about the same rate of flow as that of the liquid N being added to the beaker 6. A stopcock 9 in the siphon tube 8 is used to regulate and correlate the flow rate of the constantly changing density liquid mixture G which is discharged from the Siphon tube to form a density gradient column in the graduated cylinder 12. Since the lighter liquid N is being added yto the heavier liquid M to prepare ythe constantly density changing liquid mixture G, the column forming the density gradient in the cylinder 12 is filled from the top to insure the upwardly decreasing density of the liquid mixture proportional to the changing volume (V) of the column. Care should be taken when top filling a density gradient column to direct the stream from the Siphon tube against the side of the container holding the column to minimize turbulence within the column.

In an alternative procedure, as depicted in Figure 2, a constant delivery pump 10, which advantageously may be a constant delivery pump, such as a metering type gear pump, may be employed to transfer the constantly density changing liquid mixture G and form the density gradient column by bottom lling the density gradient column in the graduated cylinder 12. A metering oriiice 11 may be used instead of a stopcock 'to control the rate of ow (U2) of the constant density changing mixture G. The liquid mixture G may be prepared in any suitable manner (not illustrated in Figure 2) which may conveniently be similar to that explained in connection with Figure 1. Since the density gradient column is being bottom filled, the constantly density liquid mixture G in Figure 2 may advantageously be prepared by mixing a heavier liquid M having, in such case, a density (G1), into a larger volume of a lighter liquid N, having an initial density (go), in an analogous but converse manner to that described in connection with the scheme depicted in Figure l. After 1ling the graduated cylinder 12 with the density gradient column, the metering orifice 11 is carefully withdrawn with minimum disturbance of the liquid mixture in the column.

The various relationships existing in density gradient columns prepared according to the method of the present invention may be expressed in the following terms wherein g is the density of the constantly density changing liquid mixture G, which is transferred to form the density gra-dient column at a uniform rate of flow U2; g1 is the relatively lower (or higher) density of the liquid N (or M) which is added at a uniform rate of ow U1 to a larger volume of liquid M (or N) having a relatively higher (or lower) initial density go; V is the changing volume of the density gradient column during its preparation; V0 is the substantially constant volume at which the constantly density changing liquid G is prepared by mixture of the starting liquids N with M, in either desired sequence; and Z is time:

gil-g1 (4) As. is apparent from analysis of the Equation 4, the relationship between g and V is not truly linear. Nevertheless, if V0 is a relatively large quantity with respect t-o the tinal value of V, and is constant as in the case when U1 equals U2, a substantially linear relationship in the density gradient column between g and V may be obtained. When the total volume of the density gradient and V0 are about the same, a suliiciently linear density gradient for most practical purposes is obtained.

This is further illustrated in the graphs depicted in i Figure 3, wherein the substantially linear characteristics of a density gradient prepared by top filling a column from a siphon according to a method similar to that described in connection with Figure l is depicted by the curve in a solid line, and the characteristics of a gradient prepared by bottom lling a column with a pump pur suant to the procedure described in connection with Figure 2 is depicted by the curve in a broken line.

As is apparent from further consideration of the foregoing expressions, a density gradient having truly linear characteristics can be obtained by operating with different 'and -dissimilar ow rates U1 or U2 or by adding a liquid having a varying density g1 in the preparation of the constantly density changing mixture G. Thus, as an example, if the rate of flow U2 is twice the rate of ilow U1 (U2=2U1) and (V0)0 represents the initial value of V0 at zero time, the solution of Equations l, 2 and 3 defines Ithe linear relationship:

As a matter of actual practice, however, the regulation of the flow rates U1 and U2 at different and dissimilar values is ia diicult matter to physically perform. Hence the preparation of truly linear density gradients is best reserved for those instances where their being available may be an absolute necessity.

Greater accuracy can be obtained in density gradients when the miscible liquids lemployed have relatively narrow differences in density and when relatively higher or taller columns having substantially uniform cross-sections are utilized for given `density ranges which may be desirable in any particular density gradient. It is convenient, as is illustrated, for the density gnadient columns to be `contained in graduated cylinders Iand like containers and it is desirable for their volumes to be in the neighborhood of at least about 500 milliliters. This permits the density or specific gravity of the liquid mixture at various levels in the column to be correlated to the graduations or markings on the container and facilitates the reading of the density Igradient, as it were, in order to determine the specic `gravity of objects which are immersed in the column.

In this connection, density gradients may be calibrated conveniently by immersing standard floats or objects of known density or speciic gravity in the column. This is illustrated in Figure 4. A graduated series of such objects Fl, F2 and F3 are immersed in the constantly density changing liquid mixture G which forms the density gradient in the graduated cylinder 12. Besides providing an excellent means for identifying the value of the density gradient at various levels, the standard floats F1, F2 and F3 permit more accurate reading of the specific gravity of a sample S, shown in suspended immersion between the floats F1 and F2, by interpolation of its value based on consideration of its relative mean position between the known values of the density gradient at the equilibrium position assumed by the suspended oats. In addition, the use of standard lioats such as F1, F2 and F3 prolong the useful life of the density gradient by constantly accommodating and indicating the gradual changes in the gradient density as they occur upon inter level dilusion of the columnar liquid mixture.

The standard floats F1, F2 and F3 for Calibrating and reading the density gradient may be any material, liquid or solid, which is immiscible with and unaffected by the mixed liquids in the column and has a known or ac- "eurately4 interminable density ortt Sneei-e; gravity. within Any two miscible liquids that are compatible with oney another and with the material whose density or specific gravity is to be measured may be employed for preparing density gradients according to the method of the present invention. As is apparent, the liquids must be selected on the basis of having appropriate separate densities for preparing density gradients within a usable or desirable range. Care should be exercised in the selection of the liquids to avoid those that tend to induce entrainment of gases and bubble formation. Many liquid mixtures have an undesirable propensity for such behavior. Merely by way of illustration, a liquid system comprised of isopropyl alcohol and diethylene glycol is especiall advantageous for preparing density gradients according to the method of the present invention for application with such polymeric materials as polyethylene.

By way of additional illustration, the specific gravities of several polyethylene samples were determined in density gradients prepared according to the method of the present invention with a gradient density mixture of isopropyl alcohol and diethylene glycol. A density gradient column, contained in a conventional 500 milliliter graduated cylinder Was employed to cover a range from about 0.915 to 0.925 grams per cubic centimeter. The density gradient was calibrated and employed at a temperature which was maintained constantly with in about 0.01 centigrade degree of 23 C. The determinations of the densities obtained for each of the samples is compared in the following table with their known densities as obtained by an exact analytical procedure.

In employing density gradients prepared according to the method of the present invention, it is beneficial to keep the column in covered containers to avoid evaporation losses which may aiect the accuracy of its upper portions. In order to avoid the use of such upper p ortions and to circumvent the possibility of errors which may arise therefrom, it may frequently be prudent to prepare density gradients to have a sufficiently wide range which is permissive of such manner of employment. It is possible to minimize evaporation losses from the density gradient by covering the top of the column with a layer of the lighter liquid in the mixture. Readings are usually more accurate if the immersed samples are permitted at least about an hour to assume equilibrium positions. While samples can usually be removed from a column by touching them with a glass rod and slowly drawing them to the surface, it is probably more expedient in most instances to prepare a new density gradient than to remove a Very large number of samples. Satisfactory density gradients can be ordinarily prepared with commonly available reagent grade materials which require no special preparation or purication for the purpose.

.Gil

Since certainchangesvandmodifrcations cani, be.; readily entered" inthenraetieeof.-thepresent; invention with. outgdep` ing` substantially fromA itsgintended Spililiand: Scope@ it 1 .tube fullvunderstoodthat all; ottleelforegoina description and. Sneeieation., be.l interpreted, as:I beine merely illustrative of.r eert-ain ofz the more preferred eine bodinients; ofv the. nyention. andA n.0. sense. or` mannerA isl it to. be construed or taken..- as being limitingf or,y ref. Strict-ive. thereof.. excepting as. it. isset: for-.th and; denedf inthe appended clairns.V

What is claimed is:

1- Method forpreparine er. density: gradient. Consisting of e, unifornllyy varying mixture ofy two,- rnis vblearid com: natible liquidsv having` diierent; densities. which, comprises continuously Changing; the 'relative proportions of the. liquids, in; a mixture to constantly change; the density.: ofi the mixture While transferring-1 without turbulence a stream of the constantly changing density liquid mixture to a columnar container.

2. The method of claim 1 wherein the constant density changing liquid mixture is continuously transferred, without turbulence, to the container.

3. Method for preparing a density gradient consisting of a uniformly varying mixture of two miscible and compatible liquids having different densities which comprises continuously incorporating, at a uniform rate, a rst liquid having a given density in a mixture maintained at a substantially constant volume with a second liquid which has a density different than the first liquid so as to constantly change the density of the mixture; and continuously transferring, without turbulence, portions of the constantly changing density mixture to fill a liquid density gradient column in a columnar container at about the same uniform rate as that at which the first liquid is added to the mixture.

4. The method of claim 3 wherein the rst liquid has a relatively lower density than the second liquid and wherein the density gradient column in the container is filled, without turbulence, from the top.

5. The method of claim 3 wherein the first liquid has a relatively greater density than the second liquid, and wherein the density gradient column in the container is lled, without turbulence, from the bottom.

6. The method of claim 3 wherein the liquids are isopropyl alcohol and diethylene glycol.

7. Method for preparing a density gradient having substantially linear characteristics and consisting of two miscible and compatible liquids having different densities which comprises continuously incorporating, at a given uniform rate of volume flow, a rst liquid having a density (g1) in a mixture maintained at a substantially constant volume (V0) with a second liquid which has a different initial density (go) than the first liquid so as to constantly change the density (g) of the mixture; and continuously transferring, without turbulence, portions of the constantly changing density mixture to ll a liquid density gradient column having a constantly changing volume (V) in a columnar container at about the same uniform rate as that at which the first liquid is added to the mixture wherein the characteristics of the density gradient may be expressed approximately by the formula:

8. The method of claim 7 wherein the liquids are isopropyl alcohol and diethylene glycol.

9. The method of claim 7 wherein the total volume of the density gradient lled in the columnar container is about equal to the substantially constant volume of the mixture which is maintained.

l0. The method of claim 7 wherein the total volume of the density gradient lled in the columnar container is about equal to the substantially constant volume of the mixture and is in an amount of at least about 500 milliliters.

1l. Method for preparing a density gradient having linear characteristics and consisting of two miscible and compatible liquids having different densities which com prises continuously incorporating, at a rate of volume ow (U1), a first liquid having a constant density in a variable volume of a mixture with a second liquid which has a different initial density than the irst liquid so as to constantly change the density (g) of the mixture; and continuously transferring, without turbulence, portions of the constantly changing density mixture to fill a liquid density gradient column having a constantly changing volume (V) in a uniformly-cross sectioned columnar container at a uniform rate of volume flow (U2) which is different and dissimilar to the rate of flow (U1) at which the first liquid is added to the mixture in such a manner that a linear relationship between (g) and (V) is obtained in the density gradient column.

References Cited in the le of this patent UNITED STATES PATENTS 1,159,889 Benjamin Nov. 9, 1915 1,550,412 Albrecht et al Aug. 18, 1925 2,396,470 Mortensen Mar. 12, 1946 OTHER REFERENCES Determination of the Specific Gravities of Minimal Amounts of Liquids etc., Exton- Transactions of American Urological Assn., vol. XII, 1920. Reprint by Laboratory of Prudential Insurance Company of America, Newark, New Jersey (93 pages) (pages 9() and 91 of printed matter and Plate II of drawing cited). 

3. METHOD FOR PREPARING A DENSITY GRADIENT CONSISTING OF A UNIFORMLY VARYING MIXTURE OF TWO MISCIBLE AND COMPATIBLE LIQUIDS HAVING DIFFERENT DENSITIES WHICH COMPRISES CONTINUOUSLY INCORPORATING, AT A UNIFORM RATE, A FIRST LIQUID HAVING A GIVEN DENSITY IN A MIXTURE MAINTAINED AT A SUBSTANTIALLY CONSTANT VOLUME WITH A SECOND LIQUID WHICH HAS A DENSITY DIFFERENT THAN THE FIRST LIQUID SO AS TO CONSTANTLY CHANGE THE DENSITY OF THE MIXTURE; AND CONTINUOUSLY TRANSFERRING, WITHOUT TURBULENCE, PORTIONS OF THE CONSTANTLY CHANGING DENSITY MIXTURE TO FILL A LIQUID DENSITY GRADIENT COLUMN IN A COLUMNAR CONTAINER AT ABOUT THE SAME UNIFORM RATE AS THAT AT WHICH THE FIRST LIQUID IS ADDED TO THE MIXTURE. 